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Poroelasticity

Defining Poroelasticity

Poroelasticity is the term used to describe the interaction between fluid flow and solids deformation within a porous medium. As their name indicates, porous materials are solid structures comprised of pores or voids. This type of material is typically associated with natural objects, such as rocks and solids, as well as biological tissues, foams, ceramics, and paper products.

When an external load is applied to a porous medium, the volume fraction of the pores is affected. The fluid-filled pores experience a change in pressure under this mechanical stress, which, in turn, leads to fluid motion. As a reaction to this change in pore volume, the solid material shifts and deforms elastically.

From left to right, graph showing sediment displacement after two years, five years, and ten years.

Modeling Fluid Flow in Porous Materials

Modeling poroelasticity requires the coupling of two laws. The first of these is Darcy's law, which describes the relation between fluid motion and pressure within a porous medium. According to this law, the fluid velocity is directly proportional to the difference in pressure over a given distance and the fluid's viscous properties and the porous material's ability to disrupt the flow. The second law is the structural displacement of the porous matrix. Biot poroelasticity describes this coupled physics.

Real-World Application

Take an oil reservoir, for instance. Pore pressure decreases as fluid is pumped out and the reduction in pore pressure generates fluid movement. This reduces the in-situ stress, which leads to a gradual deformation in the overburden above the reservoir, causing layers to cave in or sink. This process is known as subsidence. As the images show, the deformation in porous materials progresses and becomes more pronounced over time.